Hi Jed, - It’s incompressible flow but the equations are not singular, we’re using a Poisson equation for the pressure. - It’s a centered/collocated grid. - Complex because we’re seeking solutions under a wave form with complex wavenumbers in the exponential, the right hand side is also complex.
Thibaut > On 21 Sep 2018, at 04:13, Jed Brown <[email protected]> wrote: > > "Appel, Thibaut" <[email protected]> writes: > >> Dear users, >> >> I’m having trouble finding a PC/KSP pair that works for my problem in >> parallel. >> I’m solving linearized Navier-Stokes PDE’s discretized with a finite >> difference method in 2D or 3D in a logically rectangular grid, in complex >> arithmetic. > > Compressible or incompressible? Staggered or centered grid? Why complex > arithmetic? > >> It obviously works fine with a direct solver but also with GMRES + ILU(3) in >> sequential. >> >> I tried different combinations such as >> -ksp_type gmres -pc_type asm -sub_pc_type ilu >> -ksp_type gmres -pc_type bjacobi -sub_pc_type ilu >> >> but cannot get the relative residuals below 10^(-2), after 2,000 iterations >> - even with increasing the number of ILU fill-in levels (up to 5), the >> number of GMRES restarts (300 to 1000), options such as >> -ksp_initial_guess_nonzero or -ksp_gmres_cgs_refinement_type refine_always. >> -ksp_monitor_true_residual does not seem to give more information? >> Maybe there’s room for more experimentation but if you could suggest a way >> to have a better diagnostic? >> >> With the different equation sets I’m working with, the condition numbers >> estimated with the petsc faq method vary between 10^3 and 10^7. >> On top of that I have ridiculous fill-in and have to set -pc_factor_fill to >> 14, up to 35 (!) sometimes. >> >> For our application we need a lot of discretization points in one spatial >> direction and I read somewhere that condition number scales with the square >> of discretization steps for FD methods. But is there a way to reduce it in >> my case? >> I’m also aware that fill-in should be inevitably expected when you have a >> sparse matrix with a banded structure arising from a FDM. But I was >> wondering if there’s something more I can do on the numerical side to, on >> reduce fill-in and/or help the iterative solver to converge faster? >> >> I know my discretized PDE’s + boundary conditions are scaled consistently >> with regards to matrix entries. >> I’m using natural ordering (if my unknowns are a_ij, b_ij the unknown vector >> starts with a_00 b_00 a_10 b_10 a_20 b_20 and ends with a_nxny b_nxny…) but >> I do not think this has any impact? >> >> Thanks for your support, >> >> >> Thibaut
